1. A Taste of Robot Localization Course Summary
Introduction to ROBOTICS
A Taste of Robot Localization Course Summary
Dr. John (Jizhong) Xiao
Department of Electrical Engineering
City College of New York

2. Topics Brief Review (Robot Mapping) A Taste of Localization Problem
Course Summary

3. Mapping/Localization
Answering robotics’ big questions
How to get a map of an environment with imperfect sensors (Mapping)
How a robot can tell where it is on a map (localization)
It is an on-going research
It is the most difficult task for robot
Even human will get lost in a building!

4. Review: Use Sonar to Create Map
What should we conclude if this sonar reads 10 feet?
there isn’t something here
there is something somewhere around here
10 feet
Local Map
unoccupied
no information
occupied

5. What is it a map of? Several answers to this question have been tried:
cell (x,y) is occupied
cell (x,y) is unoccupied
It’s a map of occupied cells.
oxy
oxy
pre ‘83
What information should this map contain, given that it is created with sonar ?
Each cell is either occupied or unoccupied -- this was the approach taken by the Stanford Cart.

6. What is it a map of ?
Several answers to this question have been tried:
oxy
cell (x,y) is occupied
cell (x,y) is unoccupied
oxy
pre ‘83
It’s a map of occupied cells.
It’s a map of probabilities: p( o | S1..i )
p( o | S1..i )
The certainty that a cell is occupied, given the sensor readings S1, S2, …, Si
‘83 - ‘88
The certainty that a cell is unoccupied, given the sensor readings S1, S2, …, Si
The odds of an event are expressed relative to the complement of that event.
It’s a map of odds.
evidence = log2(odds)
probabilities
p( o | S1..i )
The odds that a cell is occupied, given the sensor readings S1, S2, …, Si
odds( o | S1..i ) =
p( o | S1..i )

7. Combining Evidence So, how do we combine evidence to create a map?
The key to making accurate maps is combining lots of data.
So, how do we combine evidence to create a map?
What we want --
odds( o | S2  S1)
the new value of a cell in the map after the sonar reading S2
What we know --
odds( o | S1)
the old value of a cell in the map (before sonar reading S2)
p( Si | o ) & p( Si | o )
the probabilities that a certain obstacle causes the sonar reading Si

8. Update step = multiplying the previous odds by a precomputed weight.
Combining Evidence
The key to making accurate maps is combining lots of data.
p( o | S2  S1 )
def’n of odds
odds( o | S2  S1) =
p( o | S2  S1 )
p( S2  S1 | o ) p(o) =
Bayes’ rule (+)
p( S2  S1 | o ) p(o)
p( S2 | o ) p( S1 | o ) p(o)
conditional independence of S1 and S2 =
p( S2 | o ) p( S1 | o ) p(o)
p( S2 | o ) p( o | S1 ) =
Bayes’ rule (+)
p( S2 | o ) p( o | S1 )
precomputed values
previous odds
the sensor model
Update step = multiplying the previous odds by a precomputed weight.

9. Mapping Using Evidence Grids
represent space as a collection of cells, each with the odds (or probability) that it contains an obstacle
evidence = log2(odds)
Lab environment
likely free space
likely obstacle
lighter areas: lower evidence of obstacles being present
not sure
darker areas: higher evidence of obstacles being present

10. Mobot System Overview high-level
Abstraction level
Motor Modeling: what voltage should I set now ?
Control (PID): what voltage should I set over time ?
Kinematics: if I move this motor somehow, what happens in other coordinate systems ?
Motion Planning: Given a known world and a cooperative mechanism, how do I get there from here ?
Bug Algorithms: Given an unknowable world but a known goal and local sensing, how can I get there from here?
Mapping: Given sensors, how do I create a useful map?
low-level
high-level
Localization: Given sensors and a map, where am I ?
Vision: If my sensors are eyes, what do I do?

11. Content Brief Review (Robot Mapping) A Taste of Localization Problem
Course Summary

12. What’s the problem? WHERE AM I? But what does this mean, really?
Frame of reference is important
Local/Relative: Where am I vs. where I was?
Global/Absolute: Where am I relative to the world frame?
Location can be specified in two ways
Geometric: Distances and angles
Topological: Connections among landmarks

13. Localization: Absolute
Proximity-To-Reference
Landmarks/Beacons
Angle-To-Reference
Visual: manual triangulation from physical points
Distance-From-Reference
Time of Flight
RF: GPS
Acoustic:
Signal Fading
EM: Bird/3Space Tracker
RF:

14. Triangulation Sea Land Landmarks Works great -- as long as there
are reference points!
Lines of Sight
Unique Target
Sea

15. Compass Triangulation
cutting-edge 12th century technology
Land
Landmarks
Lines of Sight
North
Unique Target
Sea

16. Localization: Relative
If you know your speed and direction, you can calculate where you are relative to where you were (integrate).
Speed and direction might, themselves, be absolute (compass, speedometer), or integrated (gyroscope, Accelerometer)
Relative measurements are usually more accurate in the short term -- but suffer from accumulated error in the long term
Most robotics work seems to focus on this.

17. Localization Methods Markov Localization: Monte-Carlo methods
Represent the robot’s belief by a probability distribution over possible positions and uses Bayes’ rule and convolution to update the belief whenever the robot senses or moves
Monte-Carlo methods
Kalman Filtering
SLAM (simultaneous localization and mapping) ….

18. Markov Localization What is Markov Localization ?
Special case of probabilistic state estimation applied to mobile robot localization
Initial Hypothesis:
Static Environment
Markov assumption
The robot’s location is the only state in the environment which systematically affects sensor readings
Further Hypothesis
Dynamic Environment

19. Markov Localization
Instead of maintaining a single hypothesis as to where the robot is, Markov localization maintains a probability distribution over the space of all such hypothesis
Uses a fine-grained and metric discretization of the state space

20. Example Assume the robot position is one- dimensional
The robot is placed
somewhere in the
environment but it is not told its location
The robot queries its
sensors and finds out it is next to a door

21. Example
The robot moves one meter forward. To account for inherent noise in robot motion the new belief is smoother
The robot queries its
sensors and again it finds itself next to a door

22. Basic Notation
Bel(Lt=l ) Is the probability (density) that the robot assigns to the possibility that its location at time t is l
The belief is updated in response to two different types of events:
• sensor readings,
• odometry data

23. Notation
Goal:

24. Markov assumption (or static world assumption)

25. Markov Localization

26. Update Phase a b c

27. Update Phase

28. Prediction Phase

29. Summary

30. Markov Localization
Topological (landmark-based, state space organized according to the topological structure of the environment)
Grid-Based (the world is divided in cells of fixed size; resolution and precision of state estimation are fixed beforehand)
The latter suffers from computational overhead

31. Content Brief Review (Robot Mapping) A Taste of Localization Problem
Course Summary

32. Mobile Robot

33. Mobile Robot Locomotion
Locomotion: the process of causing a robot to move
Differential Drive
Tricycle R
Swedish Wheel
Synchronous Drive
Ackerman Steering
Omni-directional

34. Differential Drive Kinematic equation Nonholonomic Constraint
Property: At each time instant, the left and right wheels must follow a trajectory that moves around the ICC at the same angular rate , i.e.,
Kinematic equation
(Eq1)
Nonholonomic Constraint
(Eq2)
Eq1-Eq2

35. Differential Drive Basic Motion Control Straight motion
R : Radius of rotation
Straight motion
R = Infinity VR = VL
Rotational motion
R = VR = -VL

36. Tricycle Steering and power are provided through the front wheel
control variables:
angular velocity of steering wheel ws(t)
steering direction α(t)
d: distance from the front wheel to the rear axle

37. Tricycle Kinematics model in the world frame
---Posture kinematics model

38. Synchronous Drive All the wheels turn in unison
All wheels point in the same direction and turn at the same rate
Two independent motors, one rolls all wheels forward, one rotate them for turning
Control variables (independent)
v(t), ω(t)

39. Ackerman Steering (Car Drive)
The Ackerman Steering equation: : R

40. Car-like Robot
Driving type: Rear wheel drive, front wheel steering X Y   l
ICC R
Rear wheel drive car model:
: forward velocity of the rear wheels
: angular velocity of the steering wheels
non-holonomic constraint:
l : length between the front and rear wheels

41. Robot Sensing Collect information about the world
Sensor - an electrical/mechanical/chemical device that maps an environmental attribute to a quantitative measurement
Each sensor is based on a transduction principle - conversion of energy from one form to another
Extend ranges and modalities of Human Sensing

42. Resistive Light Sensor
Gas Sensor
Accelerometer
Gyro
Metal Detector
Pendulum Resistive
Tilt Sensors
Piezo Bend Sensor
Gieger-Muller
Radiation Sensor
Pyroelectric Detector
UV Detector
Resistive Bend Sensors
CDS Cell
Resistive Light Sensor
Digital Infrared Ranging
Pressure Switch
Miniature Polaroid Sensor
Limit Switch
Touch Switch
Mechanical Tilt Sensors
IR Pin
Diode
IR Sensor w/lens
Thyristor
Magnetic Sensor
Polaroid Sensor Board
Hall Effect
Magnetic Field
Sensors
IR Reflection
Sensor
Magnetic Reed Switch
IR Amplifier Sensor
IRDA Transceiver
IR Modulator
Receiver
Lite-On IR
Remote Receiver
Radio Shack
Remote Receiver
Solar Cell
Compass
Compass
Piezo Ultrasonic Transducers

43. Sensors Used in Robot Resistive sensors:
bend sensors, potentiometer, resistive photocells, ...
Tactile sensors: contact switch, bumpers…
Infrared sensors
Reflective, proximity, distance sensors…
Ultrasonic Distance Sensor
Motor Encoder
Inertial Sensors (measure the second derivatives of position)
Accelerometer, Gyroscopes,
Orientation Sensors: Compass, Inclinometer
Laser range sensors
Vision, GPS, …

44. Motion Planning Path Planning: Find a path connecting an
initial configuration to goal configuration
without collision with obstacles
Configuration Space
Motion Planning Methods
Roadmap Approaches
Cell Decomposition
Potential Fields
Bug Algorithms

45. Motion Planning Motion Planning Methodololgies – Roadmap
– Cell Decomposition
– Potential Field
• Roadmap
– From Cfree a graph is defined (Roadmap)
– Ways to obtain the Roadmap
• Visibility graph
• Voronoi diagram
• Cell Decomposition
– The robot free space (Cfree) is decomposed into simple regions (cells)
– The path in between two poses of a cell can be easily generated
• Potential Field
– The robot is treated as a particle acting under the influence of a potential field U,
where:
• the attraction to the goal is modeled by an additive field
• obstacles are avoided by acting with a repulsive force that yields a negative field
Global methods
Local methods

46. Full-knowledge motion planning
Roadmaps
Cell decompositions
visibility graph
exact free space represented via convex polygons
voronoi diagram
approximate free space represented via a quadtree

47. Potential field Method
Usually assumes some knowledge at the global level
The goal is known; the obstacles sensed
Each contributes forces, and the robot follows the resulting gradient.

48. Thank you! Next Week: Final Exam
Time: Dec. 13, 6:30pm-9:00pm, Place: T512
Coverage: Mobile Robot, Close-book with 1 page cheat sheet